What is the integral from 2y^2-2 to y^2+y of y ?

The integral from 2y^2-2 to y^2+y of y is (-3y^4+2y^3+9y^2-4)/2

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integral from 2y^2-2 to y^2+y of y

\int_{2 y^{2} - 2}^{y^{2} + y} y d y

\frac{- 3 y ^{4} + 2 y ^{3} + 9 y ^{2} - 4}{2}

Solution steps

\int_{2 y^{2} - 2}^{y^{2} + y} y d y

Apply the Power Rule

: [\frac{y ^{2}}{2}]_{2 y^{2} - 2}^{y^{2} + y}

= [\frac{y ^{2}}{2}]_{2 y^{2} - 2}^{y^{2} + y}

Compute the boundaries:

\frac{( y ^{2} + y ) ^{2}}{2} - \frac{( 2 y ^{2} - 2 ) ^{2}}{2}

= \frac{( y ^{2} + y ) ^{2}}{2} - \frac{( 2 y ^{2} - 2 ) ^{2}}{2}

Simplify

= \frac{- 3 y ^{4} + 2 y ^{3} + 9 y ^{2} - 4}{2}

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What is the integral from 2y^2-2 to y^2+y of y ?
The integral from 2y^2-2 to y^2+y of y is (-3y^4+2y^3+9y^2-4)/2